Broadly speaking, closure modeling in fluid flow simulations refers to parameterizing the interactions between high-fidelity and coarse-grained descriptions. Although projection based ROMs have been utilized extensively in many fluid dynamics applications [1]}, [2]}, [3]}, [4]}, they might yield inaccurate results when they are used in the under-resolved regime, i.e., when the number of modes is not large enough to capture the parameterized or transient dynamics of the underlying system [5]}. Prior studies have suggested that closure models are efficacious in decreasing such modal truncation errors [4]}. In fact, ROM closures can be viewed as correction or residual terms that are added to classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations.
